Merge objects with intersecting co-planar faces?
In this specific situation you can ...


Add Remesh modifier (Octree 3), Apply
Select all vertices and X Limited Disolve
W Merge by Distance
Select two vertices of hole and X Disolve Vertices




For some reason I lost two corner edges in N-gon (probably to much disolving :) ).  To fix it ...


Select all vertices Triangulate Ctrl+T 
Select all vertices and X Limited Disolve again